Search NASA⌕ Search

SEARCH · Search NASA

Results for “Analytic linearization”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 127 records · Page 7

Wave induced density modification in RF sheaths and close to wave launchers

With the return to full metal walls - a necessary step towards viable fusion machines - and due to the high power densities of current-day ICRH (Ion Cyclotron Resonance Heating) or RF (radio frequency) antennas, there is ample renewed interest in exploring the reasons for wave-induced sputtering and formation of hot spots. Moreover, there is experimental evidence on various machines that RF waves influence the density profile close to the wave launchers so that waves indirectly influence their own coupling efficiency. The present study presents a return to first principles and describes the wave-particle interaction using a 2-time scale model involving the equation of motion, the continuity equation and the wave equation on each of the time scales. Through the changing density pattern, the fast time scale dynamics is affected by the slow time scale events. In turn, the slow time scale density and flows are modified by the presence of the RF waves through quasilinear terms. Although finite zero order flows are identified, the usual cold plasma dielectric tensor - ignoring such flows - is adopted as a first approximation to describe the wave response to the RF driver. The resulting set of equations is composed of linear and nonlinear equations and is tackled in 1D in the present paper. Whereas the former can be solved using standard numerical techniques, the latter require special handling. At the price of multiple iterations, a simple ’derivative switch-on’ procedure allows to reformulate the nonlinear problem as a sequence of linear problems. Analytical expressions allow a first crude assessment - revealing that the ponderomotive potential plays a role similar to that of the electrostatic potential arising from charge separation - but numerical implementation is required to get a feeling of the full dynamics. A few tentative examples are provided to illustrate the phenomena involved.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Analytical model for quasi-linear flow response to resonant magnetic perturbation in resistive-inertial and viscous-resistive regimes

In this work, a quasi-linear model for plasma flow response to the resonant magnetic perturbation (RMP) in a tokamak has been rigorously developed in the resistive-inertial (RI) and viscousresistive (VR) regimes purely from the two-field reduced MHD model. Models for plasma response to RMP are commonly composed of equations for the resonant magnetic field response (i.e. the magnetic island) and the torque balance of plasma flow. However, in previous plasma response models, the magnetic island and the torque balance equations are often derived separately from reduced MHD and full MHD equations, respectively. By contrast, in this work we derive both the magnetic island response and the torque balance equations in a quasi-linear model for plasma flow response entirely from a set of two-field reduced MHD equations. Such a quasi-linear model can recover previous plasma flow response models within certain limits and approximations. Furthermore, the physical origins of quasi-linear forces and moments in the flow response equation are also accurately calculated and clarified self-consistently.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

SU-E-I-40: New Method for Measurement of Task-Specific, High-Resolution Detector System Performance

Purpose: Although generalized linear system analytic metrics such as GMTF and GDQE can evaluate performance of the whole imaging system including detector, scatter and focal-spot, a simplified task-specific measured metric may help to better compare detector systems. Methods: Low quantum-noise images of a neuro-vascular stent with a modified ANSI head phantom were obtained from the average of many exposures taken with the high-resolution Micro-Angiographic Fluoroscope (MAF) and with a Flat Panel Detector (FPD). The square of the Fourier Transform of each averaged image, equivalent to the measured product of the system GMTF and the object function in spatial-frequency space, was then divided by the normalized noise power spectra (NNPS) for each respective system to obtain a task-specific generalized signal-to-noise ratio. A generalized measured relative object detectability (GM-ROD) was obtained by taking the ratio of the integral of the resulting expressions for each detector system to give an overall metric that enables a realistic systems comparison for the given detection task. Results: The GM-ROD provides comparison of relative performance of detector systems from actual measurements of the object function as imaged by those detector systems. This metric includes noise correlations and spatial frequencies relevant to the specific object. Additionally, the integration bounds for the GM-ROD can be selected to emphasis the higher frequency band of each detector if high-resolution image details are to be evaluated. Examples of this new metric are discussed with a comparison of the MAF to the FPD for neuro-vascular interventional imaging. Conclusion: The GM-ROD is a new direct-measured task-specific metric that can provide clinically relevant comparison of the relative performance of imaging systems. Supported by NIH Grant: 2R01EB002873 and an equipment grant from Toshiba Medical Systems Corporation.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

In-Situ Statistical Analysis of Autotune Simulation Data using Graphical Processing Units

Developing accurate building energy simulation models to assist energy efficiency at speed and scale is one of the research goals of the Whole-Building and Community Integration group, which is a part of Building Technologies Research and Integration Center (BTRIC) at Oak Ridge National Laboratory (ORNL). The aim of the Autotune project is to speed up the automated calibration of building energy models to match measured utility or sensor data. The workflow of this project takes input parameters and runs EnergyPlus simulations on Oak Ridge Leadership Computing Facility’s (OLCF) computing resources such as Titan, the world’s second fastest supercomputer. Multiple simulations run in parallel on nodes having 16 processors each and a Graphics Processing Unit (GPU). Each node produces a 5.7 GB output file comprising 256 files from 64 simulations. Four types of output data covering monthly, daily, hourly, and 15- minute time steps for each annual simulation is produced. A total of 270TB+ of data has been produced. In this project, the simulation data is statistically analyzed in-situ using GPUs while annual simulations are being computed on the traditional processors. Titan, with its recent addition of 18,688 Compute Unified Device Architecture (CUDA) capable NVIDIA GPUs, has greatly extended its capability for massively parallel data processing. CUDA is used along with C/MPI to calculate statistical metrics such as sum, mean, variance, and standard deviation leveraging GPU acceleration. The workflow developed in this project produces statistical summaries of the data which reduces by multiple orders of magnitude the time and amount of data that needs to be stored. These statistical capabilities are anticipated to be useful for sensitivity analysis of EnergyPlus simulations

accelerators↗

Hierarchy of simulation models for a turbofan gas engine

Steady-state and transient performance of an F-100-like turbofan gas engine are modeled by a computer program, DYNGEN, developed by NASA. The model employs block data maps and includes about 25 states. Low-order nonlinear analytical and linear techniques are described in terms of their application to the model. Experimental comparisons illustrating the accuracy of each model are presented.

Longenbaker, W. E.↗

A high-precision ab initio determination of the equilibrium geometry and force field of HOC(+)

The results of an ab initio molecular orbital investigation of the isoformyl cation, HOC(+), shape are reported. The effects of expanding the basis set to near the Hartree-Fock limit and of electron correlation were examined, and the results indicate that near the Hartree-Fock limit the HOC(+) is linear. An analytic potential function is presented, from which the calculated rotational energies are only 0.03 percent different from the experimental values. This represents a nearly two orders of magnitude reduction in error from earlier work.

Defrees, D. J.↗

Computational fluid dynamic analysis of liquid rocket combustion instability

The paper presents a computational analysis of liquid rocket combustion instability. Consideration is given to both a fully nonlinear unsteady calculation as well as a new CFD-based linearized stability analysis. An analytical solution for the linear stability problem in a constant area combustion chamber with uniform mean flow is developed to verify the numerical analyses.

Venkateswaran, Sankaran↗

A variational approach to three-dimensional elasticity solutions of laminated composite plates

The displacements in a laminated composite are represented as products of two sets of unknown functions, one of which is only a function of the thickness coordinate and the other is a function of the in-plane coordinates (i.e., separation of variables approach), and the minimization of the total potential energy is reduced to a sequence of iterative linear problems. Analytical solutions are developed for cross-ply and angle-ply laminated composite rectangular plates. The solution for simply-supported cross-ply plates under sinusoidal transverse load reduces to that of Pagano. Numerical results for stresses and is placements for antisymmetric angle-ply laminates are presented. The three-dimensional elasticity solutions developed are important because they can be used to study the behavior of composite laminates, in addition to serving as reference for approximate solutions by numerical methods and two-dimensional theories.

Savoia, M.↗

Structural Benchmark Testing of Superalloy Lattice Block Subelements Completed

Superalloy lattice block panels, which are produced directly by investment casting, are composed of thin ligaments arranged in three-dimensional triangulated trusslike structures (see the preceding figure). Optionally, solid panel face sheets can be formed integrally during casting. In either form, lattice block panels can easily be produced with weights less than 25 percent of the mass of a solid panel. Inconel 718 (IN 718) and MarM-247 superalloy lattice block panels have been developed under NASA's Ultra-Efficient Engine Technology Project and Higher Operating Temperature Propulsion Components Project to take advantage of the superalloys' high strength and elevated temperature capability with the inherent light weight and high stiffness of the lattice architecture (ref. 1). These characteristics are important in the future development of turbine engine components. Casting quality and structural efficiency were evaluated experimentally using small beam specimens machined from the cast and heat treated 140- by 300- by 11-mm panels. The matrix of specimens included samples of each superalloy in both open-celled and single-face-sheet configurations, machined from longitudinal, transverse, and diagonal panel orientations. Thirty-five beam subelements were tested in Glenn's Life Prediction Branch's material test machine at room temperature and 650 C under both static (see the following photograph) and cyclic load conditions. Surprisingly, test results exceeded initial linear elastic analytical predictions. This was likely a result of the formation of plastic hinges and redundancies inherent in lattice block geometry, which was not considered in the finite element models. The value of a single face sheet was demonstrated by increased bending moment capacity, where the face sheet simultaneously increased the gross section modulus and braced the compression ligaments against early buckling as seen in open-cell specimens. Preexisting flaws in specimens were not a discriminator in flexural, shear, or stiffness measurements, again because of redundant load paths available in the lattice block structure. Early test results are available in references 2 and 3; more complete analyses are scheduled for publication in 2004.

Source record↗

Issues in Equation of State data generation for Hot Dense MatterA Note on Generalized Radial Mesh Generation for Plasma Electronic Structure

Precise electronic structure calculations of ions in plasmas benefit from optimized numerical radial meshes. A new closed form expression for obtaining non-linear parameters for the efficient generation of analytic log-linear radial meshes is presented. In conjunction with the (very simple) algorithm for the rapid high precision evaluation of Lambert's W-function, the above identity allows the precise construction of generalized log-linear radial meshes adapted to various constraints.

74 ATOMIC AND MOLECULAR PHYSICS↗

Asymptotic Linearity of Optimal Control Modification Adaptive Law with Analytical Stability Margins

Optimal control modification has been developed to improve robustness to model-reference adaptive control. For systems with linear matched uncertainty, optimal control modification adaptive law can be shown by a singular perturbation argument to possess an outer solution that exhibits a linear asymptotic property. Analytical expressions of phase and time delay margins for the outer solution can be obtained. Using the gradient projection operator, a free design parameter of the adaptive law can be selected to satisfy stability margins.

Nguyen, Nhan T.↗

Type B 3-fold supersymmetry and non-polynomial invariant subspaces

We obtain the most general type B 3-fold supersymmetry by solving directly the intertwining relation. We then show that it is a necessary and sufficient condition for a second-order linear differential operator to have three linearly independent local analytic solutions. We find that there are eight linearly independent non-trivial linear differential operators of this kind. As a by-product, we find new quasi-solvable second-order operators preserving a monomial or polynomial subspace, one in type B, two in type C, and four in type X{sub 2}, all of which have been missed in the existing literature. In addition, we show that type A, type B, and type C 3-fold supersymmetries are connected continuously via one parameter. A few new quasi-solvable models are also presented.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Erratum: “Nonlinear modeling of forced magnetic reconnection in slab geometry with NIMROD” [Phys. Plasmas 24, 052508 (2017)]

The linear layer response time is evaluated inappropriately in Ref. 1. This affects analytic predictions for linear and quasilinear magnetic field penetration due to a resonant, externally applied field according to Eqs. (14) and (19) of Ref. 1, respectively. The linear layer response time for the visco-resistive regime is given according to Ref. 2 as $τ_{VR}$ =2.104$τ_{shA}$S$^{2/3}_{sh}$P$^{1/6}_{m}$, where $τ_{shA}$ ≡ $τ_A$/$k_ya$ is the local shear Alfvén time at the rational surface (called the local hydromagnetic time $τ_H$ in Ref. 2) and S sh =$Sk_ya$ is the local Lundquist number. However, Ref. 1 inadvertently omits the factor of $k_y$a in $τ_{shA}$, evaluating $τ_{VR}$ using the Alfvén time τA based on the sheared magnetic field strength at the computation boundary. The proper evaluation of $τ_{VR}$ results in a linear layer response time that is ($k_ya$) 1/3 =π -1/3 ≃0.68 shorter than that in Ref. 1. The value of the time $τ'_{VR}$ used to predict quasilinear equilibria according to Eq. (19) is shorter by the same factor. Using the correct value of $τ_{VR}$ has a direct effect on analytic predictions for the magnitude and phase of the linear penetrated field, consistent with Eq. (14) in Ref. 1. Figure 1 replaces Fig. 5 of Ref. 1, exhibiting even better agreement between NIMROD computations and analytic predictions. The highest percent difference in penetrated field magnitude is 11% and in phase is 8%.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗